A reduced-complexity successive-cancellation decoding algorithm for polar codes

Abstract

Polar codes are codes which provably achieve the capacity of arbitrary symmetric binary-input channels with the complexity of encoders and decoders O(N log N), where N is the code block-length. In the paper, we will focus on a lower complexity implementation of decoding algorithm in the log-likelihood ratio domain. We use the update rule proposed by Gallager in the decoding algorithm of low density parity check (LDPC) codes to replace the node update rules used in successive cancellation (SC) algorithm for polar codes. To simplify the logarithmic and the exponential operations in the Gallager's approach node updates rule for polar codes, we further utilize a piece-wise linear algorithm to approximate the involution transform function, where the piece-wise linear algorithm only uses multiplication and addition operation. It has resulted in a reduced complexity SC decoding algorithm for polar codes. The numerical simulations show that our proposed SC algorithm (Piece-wise approx.) has a lower implementation complexity for polar code decoding, but at the cost about 0.7dB degradation in the bit-error-rate (BER) performance in comparison with the SC algorithm proposed by Arikan when the BER is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . The proposed SC algorithm (Piece-wise approx.) is a tradeoff between the error performance and the decoding complexity.